• Communications for Statistical Applications and Methods
• /
• 제26권6호
• /
• pp.611-622
• /
• 2019

This paper considers the estimation of the long memory parameter in nonparametric regression with strongly correlated errors. The key idea is to minimize a unified mean squared error of long memory parameter to select both kernel bandwidth and the number of frequencies used in exact local Whittle estimation. A unified mean squared error framework is more natural because it provides both goodness of fit and measure of strong dependence. The block bootstrap is applied to evaluate the mean squared error. Finite sample performance using Monte Carlo simulations shows the closest performance to the oracle. The proposed method outperforms existing methods especially when dependency and sample size increase. The proposed method is also illustreated to the volatility of exchange rate between Korean Won for US dollar.

• Communications for Statistical Applications and Methods
• /
• 제7권2호
• /
• pp.574-574
• /
• 2000

Consider the problem of estimating regression function from a set of data which is contaminated by a long-tailed error distribution. The linear smoother is a kind of a local weighted average of response, so it is not robust against outliers. The kernel M-smoother and the lowess attain robustness against outliers by down-weighting outliers. However, the kernel M-smoother and the lowess requires the iteration for computing the robustness weights, and as Wang and Scott(1994) pointed out, the requirement of iteration is not a desirable property. In this article, we propose the robust nonparametic regression method which does not require the iteration. Robustness can be achieved not only by down-weighting outliers but also by transforming outliers. The rank transformation is a simple procedure where the data are replaced by their corresponding ranks. Iman and Conover(1979) showed the fact that the rank transformation is a robust and powerful procedure in the linear regression. In this paper, we show that we can also use the rank transformation to nonparametric regression to achieve the robustness.

• Communications for Statistical Applications and Methods
• /
• 제7권2호
• /
• pp.575-583
• /
• 2000

Consider the problem of estimating regression function from a set of data which is contaminated by a long-tailed error distribution. The linear smoother is a kind of a local weighted average of response, so it is not robust against outliers. The kernel M-smoother and the lowess attain robustness against outliers by down-weighting outliers. However, the kernel M-smoother and the lowess requires the iteration for computing the robustness weights, and as Wang and Scott(1994) pointed out, the requirement of iteration is not a desirable property. In this article, we propose the robust nonparametic regression method which does not require the iteration. Robustness can be achieved not only by down-weighting outliers but also by transforming outliers. The rank transformation is a simple procedure where the data are replaced by their corresponding ranks. Iman and Conover(1979) showed the fact that the rank transformation is a robust and powerful procedure in the linear regression. In this paper, we show that we can also use the rank transformation to nonparametric regression to achieve the robustness.

• Communications for Statistical Applications and Methods
• /
• 제19권5호
• /
• pp.721-729
• /
• 2012

Various methods control the influence of a covariate on a response variable. These methods are analysis of covariance(ANCOVA), RANK ANCOVA, ANOVA of (covariate-adjusted) residuals, and Kruskal-Wallis tests on residuals. Covariate-adjusted residuals are obtained from the overall regression line fit to the entire data set that ignore the treatment levels or factors. It is demonstrated that the methods on covariate-adjusted residuals are only appropriate when the regression lines are parallel and covariate means are equal for all treatments. In this paper, we proposed the new nonparametric method on the ANCOVA model, as applying joint placement in a one-way layout on residuals as described in Chung and Kim (2007). A Monte Carlo simulation study is adapted to compare the power of the proposed procedure with those of the previous procedure.

• Communications for Statistical Applications and Methods
• /
• 제26권1호
• /
• pp.57-67
• /
• 2019

Income distribution is a major concern in economic theory. In regional economics, it is often of interest to compare income distributions in different regions. Traditional methods often compare the income inequality of different regions by assuming parametric forms of the income distributions, or using summary statistics like the Gini coefficient. In this paper, we propose a nonparametric procedure to test for heterogeneity in income distributions among different regions, and a K-means clustering procedure for clustering income distributions based on energy distance. In simulation studies, it is shown that the energy distance based method has competitive results with other common methods in hypothesis testing, and the energy distance based clustering method performs well in the clustering problem. The proposed approaches are applied in analyzing data from China Health and Nutrition Survey 2011. The results indicate that there are significant differences among income distributions of the 12 provinces in the dataset. After applying a 4-means clustering algorithm, we obtained the clustering results of the income distributions in the 12 provinces.

• Communications for Statistical Applications and Methods
• /
• 제9권3호
• /
• pp.607-618
• /
• 2002

Crossover design is often used in clinical trials about chronic diseases like hypertension, asthma and arthritis. In this paper, we suggest nonparametric approaches of Friedman-type rank test based on Bernard-van Elteren test and of aligned method keeping the information of blocks based on the AB/BA/AA/BB crossover design. The simulation results are presented to compare experimental error and power of several methods.

• Journal of the Korean Statistical Society
• /
• 제33권4호
• /
• pp.435-447
• /
• 2004

In additive nonparametric regression, Linton and Nielsen (1995) showed that the marginal integration when applied to the local linear smoother produces a rate-optimal estimator of each univariate component function for the case where the dimension of the predictor is two. In this paper we give new formulas for the bias and variance of the marginal integration regression estimators which are valid for boundary areas as well as fixed interior points, and show the local linear marginal integration estimator is in fact rate-optimal when the dimension of the predictor is less than or equal to four. We extend the results to the case of the local polynomial smoother, too.

• Journal of the Korean Data and Information Science Society
• /
• 제9권2호
• /
• pp.357-363
• /
• 1998

In this paper we propose a nonparametric lack of fit test based on the bootstrap method for testing the null parametric linear model by using linear smoothers. Most of existing nonparametric test statistics are based on the residuals. Our test is based on the centered bootstrap residuals. Power performance of proposed bootstrap lack of fit test is investigated via Monte carlo simulation.

• 응용통계연구
• /
• 제6권2호
• /
• pp.401-408
• /
• 1993

본 논문에서는 회귀직선 기울기의 순서성에 대한 비모수적 검정법을 제안하였다. 자료의 정보를 최대한 활용하는 Potthoff 형태의 검정통계량을 붓스트랩 분산추정량으로 표준화하여 점근 분포무관 검정을 한다. 또한 제안된 검정법의 특성과 효율을 대표본과 소표본에서 비교연구하였다.

• 한국통신학회논문지
• /
• 제28권10C호
• /
• pp.958-966
• /
• 2003

동영상에서 움직이는 객체를 찾아내기 위해 프레임 차분에 기반을 둔 변화 검출 알고리즘이 많이 사용된다. 이러한 알고리즘들은 프레임의 변화를 추정된 통계적 배경 모델을 이용하여 검출한다. 그러나 이러한 추정된 배경 모델이 실제 통계적 분포와 다르면 잘못된 검출 결과들이 생성되게 된다. 본 논문에서는 오일러 수와 구조적 텐서를 이용한 개선된 변화 검출 알고리즘을 제안한다. 제안된 오일러 수에 기반을 둔 맵핑 방법은 Nonparametric 변화검출 알고리즘에 의해 잘못 검출된 결과를 감소시키는데 사용될 수 있다. 또한 본 논문에서 제안된 구조 텐서를 이용한 방법은 움직인 객체 영역 내부의 변화를 검출하는데 사용된다. 제안된 방법은 기존의 방법에 비해 Weather에서는 90%, Mother & daughter에서는 34% 그리고 Aisle에서는 43%의 검출 에러 감소 효과를 얻을 수 있음을 실험 결과로 확인한다.